Online Papers - Brian Weatherson

Indicatives and Subjunctives 347
But two problems remain for all theories saying A → B has the truth value of A ⊃ B.
First, they make some apparently true negated conditionals turn out false, such as It
is not true that if there is a nuclear war tomorrow, life will go on as normal. It is hard
to see how an appeal to Gricean pragmatics will avoid this problem. Secondly, such
theories fail the third task we set ourselves at the start of the section: explaining the
close connections between indicatives and subjunctives.
So we might be tempted to try a different path. Let’s take the data at face value
and say that A → B is true in a context if there is some S such that some person in
that context knows S, and A and S together entail B. We can formalise this claim as
follows. Let d(x, y) be the ‘distance’ from x to y. This function will satisfy few of
the formal properties of a distance relationship, so remember this is just an analogy.
Let K be the set of all propositions S known by someone in the context, W the set
of all possible worlds, and i the impossible world, where everything is true. Then d:
W × W ∪ {i} → ℜ is as follows:
If y = x then d(x, y) = 0
If y ∈ W , y �= x and ∀S: S ∈ K ⊃ y
If y = i then d(x, y) = 2
Otherwise, d(x, y) = 3
y
S, then d(x, y) = 1
Less formally, the nearest world to a world is itself. The next closest worlds are
any compatible with everything known in the context, then the impossible world,
then the possible worlds incompatible with something known in the context. It may
seem odd to have the impossible world closer than some possible worlds, but there
are two reasons for doing this. First, in the impossible world everything known to
any conversational participant is true. Secondly, putting the impossible world at this
position accounts for some examples. This is a variant on a well known case; see for
example Gibbard (1981) and Barker (1997).
Jack and Jill are trying to find out how their local representative Kim, a Democrat
from Texas, voted on a resolution at a particular committee meeting. So far, they
have not even found out whether Kim was at the meeting. Jack finds out that all
Democrats at the meeting voted against the resolution; Jill finds out that all Texans
at the meeting voted for it. When they return to compare notes, Jack can truly say If
Kim was at the meeting, she voted against the resolution, and Jill can truly say If Kim
was at the meeting, she voted for the resolution. If i is further from the actual world
than some possible world where Kim attended the meeting, these statements cannot
both be true.
It may be thought the distance function needs to be more fine-grained to account
for the following phenomena 2 . It seems possible that in each of the following pairs,
the first sentence is true and the second false.
(19) (a) If Anne goes to the party, so will Billy.
2 Lewis (1973b) makes this objection to a similar proposal for subjunctives; the objection has just as
much force here as it does in the original case.